Advertisement

Time-like geodesic structure in massive gravity

  • Ruanjing Zhang
  • Sheng Zhou
  • Juhua Chen
  • Yongjiu Wang
Research Article

Abstract

In the present paper we analyze the geodesic structure of black hole spacetime in massive gravity with the scalar charge Q representing the modification to Einstein’s general relativity. By solving the geodesic equation and analyzing the behavior of effective potential, we investigate the time-like geodesic types of the test particle around a black hole in massive gravity. At the same time, all kinds of orbits, which are allowed according to the energy levels of the effective potential, are numerically simulated in detail.

Keywords

Time-like geodesic motion Effective potential Massive gravity 

References

  1. 1.
    Zahrani, A.M.A., Frolov, V.P., Shoom, A.A.: Phys. Rev. D 87, 084043 (2013)CrossRefADSGoogle Scholar
  2. 2.
    Kagramanova, V., Eilers, K., Hartmann, B., Schaffer, I., Toma, C.: Phys. Rev. D 88, 044025 (2013)CrossRefADSGoogle Scholar
  3. 3.
    Yang, X.L., Wang, J.C.: A&A 561, A127 (2014)CrossRefADSGoogle Scholar
  4. 4.
    Linares, R., Maceda, M., Martínez-Carbajal, D.: Phys. Rev. D 92, 024052 (2015)CrossRefADSGoogle Scholar
  5. 5.
    Bhattacharya, M., Dadhich, N., Mukhopadhyay, B.: Phys. Rev. D 91, 064063 (2015)CrossRefADSGoogle Scholar
  6. 6.
    Jaklitsch, M.J., Hellaby, C., Matravers, D.R.: Gen. Relativ. Gravit. 21, 94 (1989)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cruz, N., Olivares, M., Villanueva, J.R.: Class. Quantum Gravity 22, 1167 (2005)MathSciNetCrossRefADSMATHGoogle Scholar
  8. 8.
    Podolsky, J.: Gen. Relativ. Gravit. 31, 1703 (1999)MathSciNetCrossRefADSMATHGoogle Scholar
  9. 9.
    Kraniotis, G.V.: Class. Quantum Gravity 21, 4743 (2004)MathSciNetCrossRefADSMATHGoogle Scholar
  10. 10.
    Stuchlik, Z., Calvani, M.: Gen. Relativ. Gravit. 23, 507 (1991)MathSciNetCrossRefADSGoogle Scholar
  11. 11.
    Jiao, Z.Y., Li, Y.C.: Chin. Phys. 11, 467 (2002)CrossRefADSGoogle Scholar
  12. 12.
    Chen, J.H., Wang, Y.J.: Chin. Phys. B 17, 1184 (2008)CrossRefGoogle Scholar
  13. 13.
    Chen, J.H., Wang, Y.J.: Int. J. Mod. Phys. A 25, 1439 (2010)CrossRefADSMATHGoogle Scholar
  14. 14.
    Zhou, S., Chen, J.H., Wang, Y.J.: Int. J. Mod. Phys. D 21, 1250077 (2012)CrossRefADSGoogle Scholar
  15. 15.
    Zhou, S., Zhang, R.J., Chen, J.H., Wang, Y.J.: Int. J. Theor. Phys. 54, 2905 (2015)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Brans, C., Dicke, R.H.: Phys. Rev. 124, 925 (1961)MathSciNetCrossRefADSMATHGoogle Scholar
  17. 17.
    Buchdahl, H.A.: Mon. Not. R. Astron. Soc. 150, 1 (1970)CrossRefADSGoogle Scholar
  18. 18.
    Dvali, G., Gabadadze, G., Porrati, M.: Phys. Lett. B 485, 208 (2000)MathSciNetCrossRefADSMATHGoogle Scholar
  19. 19.
    Bekenstein, J.D.: Phys. Rev. D 70, 083509 (2004)CrossRefADSGoogle Scholar
  20. 20.
    Ferraro, R., Fiorini, F.: Phys. Rev. D 78, 124019 (2008)MathSciNetCrossRefADSGoogle Scholar
  21. 21.
    Tasseten, K., Tekin, B.: arXiv:1506.03714v1 [gr-qc]
  22. 22.
    Comelli, D., Nesti, F., Pilo, L.: Phys. Rev. D 83, 084042 (2011)CrossRefADSGoogle Scholar
  23. 23.
    Riess, A.G., et al.: Astron. J. 116, 1009 (1998)CrossRefADSGoogle Scholar
  24. 24.
    Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)CrossRefADSGoogle Scholar
  25. 25.
    Dubovsky, S.L.: J. High Energy Phys. 10, 076 (2004)MathSciNetCrossRefADSGoogle Scholar
  26. 26.
    Fierz, M., Pauli, W.: Proc. R. Soc. Lond. Ser. A 173, 211 (1939)MathSciNetCrossRefADSGoogle Scholar
  27. 27.
    de Rham, C.: Living Rev. Relativ. 17, 7 (2014)ADSGoogle Scholar
  28. 28.
    Hinterbichler, K.: Rev. Mod. Phys. 84, 671 (2012)CrossRefADSGoogle Scholar
  29. 29.
    Bebronne, M.V.: arXiv:0910.4066 [gr-qc]
  30. 30.
    de Rham, C., Gabadadze, G., Tolley, A.J.: Phys. Rev. Lett. 106, 231101 (2011)CrossRefADSGoogle Scholar
  31. 31.
    Hassan, S.F., Rosen, R.A.: Phys. Rev. Lett. 108, 041101 (2012)CrossRefADSGoogle Scholar
  32. 32.
    Hassan, S.F., Rosen, R.A., Schmidt-May, A.: J. High Energy Phys. 02, 026 (2012)MathSciNetCrossRefADSGoogle Scholar
  33. 33.
    Bebronne, V.M., Peter, G.T.: J. High Energy Phys. 0904, 100 (2009)Google Scholar
  34. 34.
    Comelli, D., Crisostomi, M., Nesti, F., Pilo, L.: Phys. Rev. D 84, 104026 (2011)CrossRefADSGoogle Scholar
  35. 35.
    Fernando, S., Clark, T.: Gen. Relativ. Gravit. 46, 1834 (2014)MathSciNetCrossRefADSGoogle Scholar
  36. 36.
    Fernando, S.: Mod. Phys. Lett. A 30, 1550147 (2015)MathSciNetCrossRefADSGoogle Scholar
  37. 37.
    Capela, F., Tinyakov, P.G.: J. High Energy Phys. 04, 042 (2011)MathSciNetCrossRefADSGoogle Scholar
  38. 38.
    Capela, F., Nardini, G.: Phys. Rev. D 86, 024030 (2012)CrossRefADSGoogle Scholar
  39. 39.
    Dubovsky, S.L., Tinyakov, P.G., Tkachev, I.I.: Phys. Rev. D 72, 084011 (2005)MathSciNetCrossRefADSGoogle Scholar
  40. 40.
    Berezhiani, Z., Comelli, D., Nesti, F., Pilo, L.: Phys. Rev. Lett. 99, 131101 (2007)CrossRefADSGoogle Scholar
  41. 41.
    Berezhiani, Z., Comelli, D., Nesti, F., Pilo, L.: J. High Energy Phys. 07, 130 (2008)MathSciNetCrossRefADSGoogle Scholar
  42. 42.
    Villante, F.L., Ricci, B.: Astrophys. J. 714, 944 (2010)CrossRefADSGoogle Scholar
  43. 43.
    Choudhurry, S.R., Joshi, G.C., Mahajan, S., Mckellar, B.H.J.: Astropart. Phys. 21, 559 (2004)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Ruanjing Zhang
    • 1
  • Sheng Zhou
    • 1
  • Juhua Chen
    • 1
  • Yongjiu Wang
    • 1
  1. 1.College of Physics and Information ScienceHunan Normal UniversityChangshaChina

Personalised recommendations